Update metrics.mdx (#14181)

Author: cleptric

develop-docs/backend/application-domains/metrics.mdx

@@ -120,27 +120,3 @@ SENTRY_METRICS_OPTIONS = {
 ```
 
 Once configured, the metrics backend will emit to the DogStatsD server and then flushed periodically to Datadog over HTTPS.
-
-## Logging Backend
-
-The `LoggingBackend` reports all operations to the `sentry.metrics` logger. In addition to the metric name and value, log messages also include extra data such as the `instance` and `tags` values which can be displayed using a custom formatter.
-
-```python
-SENTRY_METRICS_BACKEND = 'sentry.metrics.logging.LoggingBackend'
-
-LOGGING['loggers']['sentry.metrics'] = {
-    'level': 'DEBUG',
-    'handlers': ['console:metrics'],
-    'propagate': False,
-}
-
-LOGGING['formatters']['metrics'] = {
-    'format': '[%(levelname)s] %(message)s; instance=%(instance)r; tags=%(tags)r',
-}
-
-LOGGING['handlers']['console:metrics'] = {
-    'level': 'DEBUG',
-    'class': 'logging.StreamHandler',
-    'formatter': 'metrics',
-}
-```